Plot hole: Nuclear Man arrives at Luthor's apt. and steps into a dark corner, where he loses his powers. From the opposite angle the place is filled with light, so Nuclear Man shouldn't have lost his strength.

Near the end of the film, Superman gives a press conference in front of a bluish mirror-glass building which is meant to be the Daily Planet skyscraper in Metropolis (which we all know is New York, sort of). The shot is framed so you can only see the bottom of the building - necessary as it is only about 3 floors high, and is in fact the railway station in Milton keynes, England, about 400 yards from where I work. Even the crowd have a vaguely British look about them - presumably passers-by were recruited and stood there in their own clothes (this would matter less now - Brits look more American than they did in the Eighties).